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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Some error estimates for the midpoint, trapezoidal and Ostrowski formulae are also given.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we shall establish some extended trapezoid-type$$\bigg|\dfrac{c-a}{b-a}f(x)+\dfrac{b-c}{b-a}f(y)-\dfrac{1}{b-a}\int_a^bf(t)dt\bigg|,\:(a\leq x\leq c\leq y\leq b)$$inequalities for differentiable convex functions and differentiable concave functions which are connected with Hermite-Hadamard inequality.
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Key Findings & Data:In this paper, we shall establish some extended trapezoid-type$$\bigg|\dfrac{c-a}{b-a}f(x)+\dfrac{b-c}{b-a}f(y)-\dfrac{1}{b-a}\int_a^bf(t)dt\bigg|,\:(a\leq x\leq c\leq y\leq b)$$inequalities for differentiable convex functions and differentiable concave functions which are connected with Hermite-Hadamard inequality.
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Conclusion & Impact:Some error estimates for the midpoint, trapezoidal and Ostrowski formulae are also given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Hermite-Hadamard Inequality · Midpoint Inequality · Trapezoid Inequality
Abstract
In this paper, we shall establish some extended trapezoid-type$$\bigg|\dfrac{c-a}{b-a}f(x)+\dfrac{b-c}{b-a}f(y)-\dfrac{1}{b-a}\int_a^bf(t)dt\bigg|,\:(a\leq x\leq c\leq y\leq b)$$inequalities for differentiable convex functions and differentiable concave functions which are connected with Hermite-Hadamard inequality. Some error estimates for the midpoint, trapezoidal and Ostrowski formulae are also given.
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Cite This Article
HWANG, S. R., TSENG, K. L. (2022). Some extended trapezoid-type inequalities and applications. Hacettepe Journal of Mathematics and Statistics, Cilt: 45 - Sayı: 3, 827–850. https://ajindex.com/articles/530178